A299505 Numbers of the form x^4 + y*x^3 + y^2*x^2 + y^3*x + y^4, where x and y are positive integers.

5, 31, 80, 121, 211, 341, 405, 496, 781, 1031, 1280, 1441, 1555, 1936, 2101, 2511, 2801, 3125, 3355, 3376, 4141, 4651, 4681, 5261, 5456, 6480, 6505, 6841, 7381, 7936, 8431, 9031, 9801, 9881, 11111, 11605, 12005, 12496, 13981, 14251, 15961, 16105, 16496, 17091, 17891

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Prog

(Julia)
function isA299505(n)
    n % 5 >= 2 && return false
    n == 5 && return true
    K = Int(floor(5.383*log(n)^1.161))
    M = Int(floor(2*sqrt(n/3)))
    for k in 3:K
        for y in 2:M, x in 1:y
            n == x^4+y*x^3+y^2*x^2+y^3*x+y^4 && return true
    end end
    return false
end
A299505list(upto) = [n for n in 1:upto if isA299505(n)]
println(A299505list(18000))

Crossrefs

Cf. A024614, A002649 (subsequence of primes).

Sequence in context: A078686 A031908 A139862 * A102732 A213068 A138657

Adjacent sequences: A299502 A299503 A299504 * A299506 A299507 A299508

Keyword

nonn

Author

Peter Luschny, Mar 02 2018

Status

approved